Your query is not simple, and you have already received some fair advice for both approaches. The foundation to base your decision on your path will likely depend on whether you have found your "forever" loudspeakers. If so, then you can go either way with each approach having pros and cons.
A well-conceived Integrated simplifies your system with fewer interconnects as "eric_squires" points out. Choosing the right integrated is then the key. For myself, I wouldn't settle on price alone as the sole criterion.
Personally, my system is built around a pair of very fine mono blocks, located near my loudspeakers and a really fine preamplifier. My preamplifier has a very low output impedance, so that it is very capable of driving quality single ended interconnects the distance required to the amps. This keeps speaker cables short.
As a sidebar, avoid placing your equipment between your loudspeakers. If I had the disposable income, I would likely choose an Ypsilon Phaethon integrated and live happily ever after. Others have provided recommendations for some other less expensive and very good options as well.
Happy hunting & listening.